"Missing the reshuffle" describes the following effect:
When you reshuffle your draw deck, there are usually cards in hand or in play. Most easily that happens when you just redraw 5 cards for your next turn, and there are less than 5 cards in your drawpile. Say you have a 12 card deck like it usually happens after the first two turns, without any cards that draw cards. Say you just bought Silver/Silver on turn 1 and 2. Now you draw two "usual" hands. In turn 5, you will draw the 2 remaining cards. These cards "miss the shuffle", as they, in contrast to the other 10 cards of the deck, will not be in the draw pile for the next shuffle. So they can only played once in two shuffles, while the other card will be played twice. If these are important cards, this of course sucks.
When this happens between turns, there is not much that can be done about it, but during your turn, you should be careful if you want to trigger a reshuffle by playing say a Smithy or not. You might give up the opportunity to buy some better card, but by triggering the reshuffle, the Smithy, all the cards in your hand and play and the newbought card might not get seen for a long time, so maybe it's better to just settle for the Gold instead of hoping for the Province. Maybe it's not...
This effect can get really strong if you have discard-for-benefit cards like Cellar. If you have say an engine playing Villages and Smithies to draw many cards, and inbetween discard Coppers and Estates with Cellars, all your good cards are in your hand and in play (the Villages, Smithies, Cellars, good Treasures, whatever), while your bad cards (Copper, Victory cards) are in your discard. In this situation it can be really dangerous to trigger a reshuffle if you can't guarantee to draw the whole remaining deck this turn, because if you do, after this turn you have a draw deck with 10 (or more) bad cards which will take some turns to get trough, while all the cards that you rely on are in your discard.